Many applications, for example, wireless systems or other communication systems, employ digital adaptive filters to reduce error caused by a communication channel. Typically, such adaptive filters include a tapped delay lines to perform a convolution operation on a series of parameters known as tap coefficients and an incoming signal. These types of adaptive filters are also known as adaptive finite impulse response (AFIR) filters. The tap coefficients typically correspond to the impulse response of a channel through which the incoming signal arrives. Thus, for time-varying channels, such adaptive (AFIR) filters need to accurately and expeditiously converge their tap coefficients to appropriate values corresponding to the varying channel characteristics.
In order to derive appropriate tap coefficients, many adaptive filters employ an algorithm known as Least Mean Square or LMS algorithm. It is evident that in time-varying applications, speed of convergence and especially, tracking of the channel becomes critical. As such, conventional LMS systems may not be sufficient to fulfill adaptive filtering requirements.
FIG. 1 illustrates a typical prior art adaptive filter that employs a Least Means Square system to calculate the tap coefficients W.sub.k based on the following recursive equation:
W.sub.k (n+1)=W.sub.k (n)+.mu.e(n)X.sub.k (nT)n=0,1,. . . L, (1)
wherein .mu. is known as a step-size signal and e(n) is the error signal and X is the received signal samples. As shown in FIG. 1, input terminal 12 is configured to receive a sequence of input signals X, which is routed through upper branch A of a tapped delay line 223. Upper branch A includes a plurality of delay elements 42, which are configured to provide a corresponding delayed version of signal X at their output terminal. The input terminal of each delay element is also coupled to a corresponding multiplier 40 that is configured to multiply the delayed version of signal X with a corresponding tap weight. The output terminals of each multiplier 40 is coupled to a corresponding adder 50, so as to accumulate the numbers generated by the multipliers along branch C. The accumulated value is provided to an input terminal of a subtractor 54, which is configured to generate an error signal e.
The other input of subtractor 54 is coupled to a reference signal 52, which corresponds to a series of training signals that are expected to be received by the receiver. In situations wherein training signals are not available, the output signal generated by the tapped delay line is provided to a slicer circuit (not shown) and in turn to subtractor 54. The error signal is provided to a step size multiplier 53, which is configured to multiply the error signal by a step size .mu..
The output terminal of step size multiplier 53 is coupled to a plurality of tap weight generating branches 55, which are configured to provide a tap weight signal or tap coefficient to each of the multipliers 40.
Each tap weight generating branch comprises a multiplier 18 having one input terminal coupled to the output terminal of step size multiplier 53. The other input terminal of each multiplier 18 is configured to receive a corresponding delayed version of signal X via the lower branch of adaptive filter 10. As such the lower branch of adaptive filter 10 includes a plurality of delay elements 44 that are configured to provide the delayed version of signal X at the same time intervals that delay elements 42 provide delayed versions of signal X at the upper branch of adaptive filter 10.
Each tap weight generating branch also comprises an integrator 32 that is coupled to the output terminal of the corresponding multiplier 18. Integrator 32 typically comprises an adder 34 coupled to a delay element 36 in a closed loop arrangement. The output terminal of integrator 32 (venerates the corresponding tap weight in each branch, and is coupled to the corresponding multiplier 40.
In an adaptive filter such as the one described in FIG. 1, the error signal may not converge substantially to zero while continuing to track the channel.
Thus, there is a need for an improved adaptive finite impulse response (AFIR) filter that employs a least Mean Square (LMS) algorithm where the error signal can converge substantially to zero.